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»
Mathematica
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Mathematics and Algorithms
>
Number Theory
>
Diophantine Equations
>
FrobeniusSolve
>
BUILT-IN MATHEMATICA SYMBOL
Solving Frobenius Equations and Computing Frobenius Numbers
Tutorials »
|
FrobeniusNumber
IntegerPartitions
Reduce
FindInstance
ExtendedGCD
See Also »
|
Additive Number Theory
Diophantine Equations
Integer Functions
New in 6.0: Mathematics & Algorithms
New in 6.0: Number Theory & Integer Functions
More About »
FrobeniusSolve
FrobeniusSolve
gives a list of all solutions of the Frobenius equation
.
FrobeniusSolve
gives at most
m
solutions.
MORE INFORMATION
The Frobenius equation is the Diophantine equation
, where the
are positive integers,
b
is an integer, and a solution
must consist of non-negative integers. For negative
b
there are no solutions.
EXAMPLES
CLOSE ALL
Basic Examples
(1)
All solutions of the Frobenius equation
:
Check:
All solutions of the Frobenius equation
:
In[1]:=
Out[1]=
Check:
In[2]:=
Out[2]=
Properties & Relations
(2)
Reduce
may also be used to find the solutions to the Frobenius equation:
FrobeniusSolve
returns the same solution set:
FrobeniusSolve
gives coefficient lists for
IntegerPartitions
:
SEE ALSO
FrobeniusNumber
IntegerPartitions
Reduce
FindInstance
ExtendedGCD
TUTORIALS
Solving Frobenius Equations and Computing Frobenius Numbers
TUTORIAL COLLECTION
Advanced Algebra
MORE ABOUT
Additive Number Theory
Diophantine Equations
Integer Functions
New in 6.0: Mathematics & Algorithms
New in 6.0: Number Theory & Integer Functions
New in 6